Society of Actuaries (SOA) PA Practice Exam

What is a significant characteristic of overdispersion affecting GLMs?

1. The model is simplified and lacks complexity

2. The variance and mean are assumed to be equal

3. The distortion of model fit due to related mean and variance

4. The model predictions become more accurate

The correct answer is: The distortion of model fit due to related mean and variance

Overdispersion refers to a situation in generalized linear models (GLMs) where the observed variance in the data is greater than what the model expects, based on a specific distribution (like Poisson). This often arises in count data, where the variability is influenced by unobserved factors. A significant characteristic of overdispersion is the distortion of model fit due to the relationship between the mean and variance. In many GLM applications, particularly with Poisson regression, the assumption is that the mean and variance are equal. However, when overdispersion occurs, this assumption fails, leading to a situation where the variance is greater than the mean. As a result, the model may provide poor predictions and inferences, as it does not properly account for this extra variability in the data. Understanding this characteristic is crucial because it highlights the need for alternative modeling strategies, such as using a negative binomial distribution that can accommodate the overdispersion, allowing for a better fit and more reliable results in analyses.